Robust H∞ control for discrete-time fuzzy systems via basis-dependent Lyapunov functions

This paper deals with the robust H∞ control problem for a class of discrete-time fuzzy systems with uncertainty. The uncertainty is assumed to be of structured linear fractional form. By using basis-dependent Lyapunov function, an H∞ control design approach is developed. The control design approach is facilitated by introducing some additional instrumental matrix variables. These additional matrix variables decouple the Lyapunov and the system matrices, which makes the control design feasible. The proposed approach leads to some sufficient results in the form of strict linear matrix inequalities (LMIs). It is expected that the basis-dependent results are less conservative than the basis-independent ones due to the introduction of basis-dependent Lyapunov function. Finally, numerical examples including the discrete chaotic Lorenz system are also given to demonstrate the applicability of the proposed approach.